> On Sat, Sep 20, 2008 at 11:58 PM,NasserAbbasi<[EMAIL PROTECTED]> wrote:
>
> > Hello;
> > I am a sage newbie. I'd like to find out how to make Sage give me
> > this same result that I get in Mathematica.
>
> > This is what I typed (I do not know how to cut/paste from the VMWare
> > player console to her yet, so if there is a typo it is because of
> > this).
>
> > f=var('f')
> > assume(f>0)
> > integral( e^(-I * 2 * pi * f * t), t , 0 , Infinity)
>
> > The answer I get starts with
>
> > limit(sin(2*pi*f*t),t, etc...etc...
>
> > Is there a way to tell Sage to give me this answer I get from
> > Mathematica?
>
> > Assuming[Im[f] < 0, Integrate[Exp[(-I)*2*Pi*f*t], {t, 0, Infinity}]]
> > -(I/(2*f*Pi))
>
> > Thanks,
> >Nasser
On Sep 21, 2:49 pm, "David Joyner" <[EMAIL PROTECTED]> wrote:
> This integral doesn't converge. Why do you think Sage should return
> what Mma does?
>
I think it does converge.
int( exp(-I 2 Pi f t),{t,0,infinity) =
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi f t) }
0
Let f be complex in general, say (a+ I b) then the above becomes
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi (a +I b) t) }
0
or
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi a t) exp (2 Pi b t) }
0
Since b<0, then the above becomes
1/(-I 2 Pi f) * [ 0 - 1 }
or
1/(I 2 Pi f)
or
-I/(2 Pi f)
which is what Mathematica gave.
Did I make a mistake in the above somewhere? Could you explain why
you think the integral does not converge?
Nasser
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